# Chapter 12.6 - PowerPoint PPT Presentation

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Chapter 12.6. Surface Area and Volume of Spheres. Concept. Surface Area of a Sphere. Example 1. Find the surface area of the sphere. Round to the nearest tenth. S =4  r 2 Surface area of a sphere =4 (4.5) 2 Replace r with 4.5. ≈254.5Simplify. Answer: 254.5 in 2.

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Chapter 12.6

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## Chapter 12.6

Surface Area and Volume of Spheres

### Concept

Surface Area of a Sphere

### Example 1

Find the surface area of the sphere. Round to the nearest tenth.

S=4r2Surface area of a sphere

=4(4.5)2Replace r with 4.5.

≈254.5Simplify.

### Example 1

Find the surface area of the sphere. Round to the nearest tenth.

A.462.7 in2

B.473.1 in2

C.482.6 in2

D.490.9 in2

Use Great Circles to Find Surface Area

### Example 2A

A. Find the surface area of the hemisphere.

Find half the area of a sphere with the radius of 3.7 millimeters. Then add the area of the great circle.

Use Great Circles to Find Surface Area

### Example 2B

B. Find the surface area of a sphere if the circumference of the great circle is 10 feet.

First, find the radius. The circumference of a great circle is 2r. So, 2r = 10 or r = 5.

Use Great Circles to Find Surface Area

### Example 2C

C. Find the surface area of a sphere if the area of the great circle is approximately 220 square meters.

First, find the radius. The area of a great circle is r2. So, r2 = 220 or r≈ 8.4.

### Example 2A

A. Find the surface area of the hemisphere.

A.110.8 m2

B.166.3 m2

C.169.5 m2

D.172.8 m2

### Example 2B

B. Find the surface area of a sphere if the circumference of the great circle is 8 feet.

A.100.5 ft2

B.201.1 ft2

C.402.2 ft2

D.804.3 ft2

### Example 2C

C. Find the surface area of the sphere if the area of the great circle is approximately 160 square meters.

A.320 ft2

B.440 ft2

C.640 ft2

D.720 ft2

### Concept

(15)3r = 15

Volumes of Spheres and Hemispheres

### Example 3A

A. Find the volume a sphere with a great circle circumference of 30 centimeters. Round to the nearest tenth.

Find the radius of the sphere. The circumference of a great circle is 2r. So, 2r = 30 or r = 15.

≈ 14,137.2 cm3

r 3

Use a calculator.

Volumes of Spheres and Hemispheres

### Example 3B

B. Find the volume of the hemisphere with a diameter of 6 feet. Round to the nearest tenth.

The volume of a hemisphere is one-half the volume of the sphere.

Volume of a hemisphere

Answer: The volume of the hemisphere is approximately 56.5 cubic feet.

### Example 3A

A. Find the volume of the sphere to the nearest tenth.

A.268.1 cm3

B.1608.5 cm3

C.2144.7 cm3

D.6434 cm3

### Example 3B

B. Find the volume of the hemisphere to the nearest tenth.

A.3351.0 m3

B.6702.1 m3

C.268,082.6 m3

D.134,041.3 m3

Solve Problems Involving Solids

### Example 4

ARCHEOLOGYThe stone spheres of Costa Rica were made by forming granodiorite boulders into spheres. One of the stone spheres has a volume of about 36,000 cubic inches. What is the diameter of the stone sphere?

UnderstandYou know that the volume of the stoneis 36,000 cubic inches.

PlanFirst use the volume formula to find theradius. Then find the diameter.

### Example 4

RECESS The jungle gym outside of Jada’s school is a perfect hemisphere. It has a volume of 4,000 cubic feet. What is the diameter of the jungle gym?

A.10.7 feet

B.12.6 feet

C.14.4 feet

D.36.3 feet